Earlier quoted context omitted.
This belief that nature has control over the planet is sadly mistaken. If humanity wanted to, it could nuke the planet eliminating all insect life. Humanity has invented things far beyond the reach of nature and far beyond what nature can cope with.
"it could nuke the planet eliminating all insect life" We'd have to spend a while building a supply of big cobalt-salted bombs because the nuclear arsenals we've actually had have come nowhere near to the level required to wipe out all people let alone all insects.
It is conceivable a few might live, but it is also entirely possible the survivors would be too irradiated to sustain a breeding populations. Vast plant populations would die off, only those not directly blasted and able to survive a few years of artificial global winter survive. This presumes the dust is also non-reflective, because if it lowers the Earth's albedo enough it could trigger an ice age. If that happens then pretty much no individuals survive the triple threat of nuclear blasting, perpetual winter and loss of vegetation, unless they have some uncommon radiation resistance and incredibly low nutrition requirements. In this last paragraph was I talking about humans or insects? Doesn't matter; the cost of nuclear war is too high for us to talk about it lightly, because it is an awesome power that can destroy us if used lightly.